DML Restriction unless through a function

Hi all;

Is it possible to write a trigger or the ilk that would disallow
direct inserts, updates, or deletes to a table unless it was
being executed through a function?  How can I identify that the
DML being issued is being done via a function?

We are writing an API of sorts and for various business logic
aspects, it is necessary that certain checks and sets of data
are processed through the database in a certain method.  The use
of functions provides the ability to do this, but I would
definitely like to restrict access to the under lying tables.

If I revoke insert,update,delete privileges on a table, would
the user still be able to affect data manipulation through a
function?  Is that another way of getting around this?

TIA